Approach of gas and radiation to equilibrium

Abstract

Einstein described equilibrium between two-level gas molecules and radiation in terms of a Brownian motion model involving frictional and agitational effects arising from photon absorptions and emissions. This paper extends his treatment to the case of disequilibrium when molecules and radiation are in cavities with either black or perfectly reflecting walls. The precise role of the black walls in promoting equilibrium is explicated in terms of Einstein’s formula for the frictional effect and the nature of changes in radiation patterns caused by Doppler shifts of photon frequencies. It is then shown that equilibrium between the two-level gas molecules and radiation cannot be achieved for a container with perfectly reflecting walls. The blockage of equilibrium occurs because a change in the slope of the Planck spectrum at the resonant frequency causes a change in the frictional force.